The owls example diagnostics were originally in the appendix, but now live in this document to minimise the length of the supplement.

Stage 1

Submodel 1 - Capture recapture

\(\psi_{1}\)

\(\alpha_{1}, \alpha_{4}\)

rowname mean sd n_eff Rhat Bulk_ESS Tail_ESS valid se_mean 1% 2.5% 10% 50% 90% 97.5% 99% Q5 Q50 Q95 MCSE_Q1 MCSE_Q2.5 MCSE_Q10 MCSE_Q50 MCSE_Q90 MCSE_Q97.5 MCSE_Q99 MCSE_SD
v[5] -1.1637215 0.3970025 29752 1.000345 29774 50348 1 0.0023016 -2.0991431 -1.950286 -1.6741696 -1.160669 -0.6571480 -0.3952717 -0.2525858 -1.8209121 -1.160669 -0.5165099 0.0060204 0.0045647 0.0034430 0.0025107 0.0030968 0.0050961 0.0055631 0.0016275
v[3] -0.0298675 0.2470921 25518 1.000286 25526 44131 1 0.0015465 -0.6093158 -0.514765 -0.3460832 -0.028905 0.2854917 0.4527495 0.5455072 -0.4355493 -0.028905 0.3746568 0.0035529 0.0028821 0.0018834 0.0016359 0.0021049 0.0033161 0.0042712 0.0010936

\(\alpha_{5, t}\)

rowname mean sd n_eff Rhat Bulk_ESS Tail_ESS valid se_mean 1% 2.5% 10% 50% 90% 97.5% 99% Q5 Q50 Q95 MCSE_Q1 MCSE_Q2.5 MCSE_Q10 MCSE_Q50 MCSE_Q90 MCSE_Q97.5 MCSE_Q99 MCSE_SD
bp[5] 0.5086961 0.7844574 63004 1.000180 63350 64774 1 0.0031266 -1.3181734 -1.0159529 -0.4776929 0.4990231 1.5090835 2.0842633 2.4050763 -0.7575012 0.4990231 1.8121690 0.0124849 0.0082018 0.0055144 0.0033047 0.0056808 0.0092535 0.0156610 0.0023994
bp[12] 1.7001173 0.9590478 65078 1.000146 67102 60223 1 0.0037591 -0.3426315 -0.0340295 0.5217426 1.6469046 2.9447041 3.7353291 4.2027545 0.2171699 1.6469046 3.3632794 0.0102126 0.0080149 0.0047402 0.0041607 0.0077367 0.0128247 0.0220208 0.0028747
bp[17] -2.2605236 1.2822024 69358 1.000139 72313 64352 1 0.0048664 -5.6630424 -5.0368963 -3.9623678 -2.1618269 -0.7013253 -0.0250960 0.3142353 -4.5302549 -2.1618269 -0.3377610 0.0249826 0.0167168 0.0100819 0.0051231 0.0065340 0.0086871 0.0115343 0.0037328
bp[7] 1.6440875 0.8175606 53630 1.000136 54121 62039 1 0.0035295 -0.1648866 0.1124377 0.6260855 1.6143076 2.7008573 3.3397728 3.7134583 0.3522940 1.6143076 3.0366474 0.0098411 0.0076894 0.0059474 0.0038998 0.0067470 0.0094944 0.0161505 0.0025568
bp[16] 2.4515667 1.2687353 63693 1.000127 66966 59675 1 0.0050240 -0.1565240 0.2140929 0.9093065 2.3557436 4.1205033 5.1996655 5.8226503 0.5399201 2.3557436 4.6847978 0.0139919 0.0086681 0.0065730 0.0053027 0.0097887 0.0165390 0.0287161 0.0038300
bp[25] 1.5740120 1.2671315 51472 1.000117 53589 56774 1 0.0055834 -0.8405487 -0.5315313 0.0758154 1.4388352 3.2780712 4.4254838 5.0679844 -0.2548834 1.4388352 3.8775319 0.0107083 0.0087598 0.0056627 0.0063082 0.0121331 0.0192154 0.0234746 0.0041397
bp[3] 1.0859111 0.7325786 59591 1.000082 59987 62758 1 0.0029998 -0.5558430 -0.3033001 0.1643164 1.0682592 2.0283953 2.5906542 2.9060265 -0.0818336 1.0682592 2.3196378 0.0109164 0.0067626 0.0040900 0.0032479 0.0051537 0.0094577 0.0112898 0.0021939
bp[23] -0.6667710 0.8621374 69551 1.000076 70335 65708 1 0.0032686 -2.8141899 -2.4322033 -1.7678687 -0.6439015 0.4063109 0.9855331 1.3008434 -2.1115524 -0.6439015 0.7113171 0.0160209 0.0107786 0.0068470 0.0037566 0.0052886 0.0085865 0.0134690 0.0026236
bp[2] 1.3342073 0.6884622 61881 1.000069 62608 62051 1 0.0027675 -0.1837483 0.0512987 0.4753865 1.3100902 2.2224096 2.7495197 3.0562782 0.2425286 1.3100902 2.5085913 0.0104780 0.0053475 0.0033296 0.0028869 0.0053767 0.0084021 0.0118336 0.0020417
bp[19] -2.3036066 1.2726245 68023 1.000067 70829 63308 1 0.0048776 -5.6832152 -5.0739472 -3.9907657 -2.2042942 -0.7604267 -0.0812469 0.2522439 -4.5526575 -2.2042942 -0.3980365 0.0226147 0.0170252 0.0102767 0.0051602 0.0060291 0.0088682 0.0139035 0.0037341
bp[4] 1.9757219 0.7549037 56053 1.000066 57145 58460 1 0.0031879 0.3728642 0.6074469 1.0392071 1.9382943 2.9569772 3.5676590 3.9147815 0.8027079 1.9382943 3.2797806 0.0088997 0.0059907 0.0040358 0.0033090 0.0062091 0.0099662 0.0161752 0.0023300
bp[13] 0.5813253 0.9092773 65864 1.000060 66545 65576 1 0.0035408 -1.5163299 -1.1761775 -0.5548206 0.5675498 1.7378573 2.4141656 2.8074627 -0.8865236 0.5675498 2.0882032 0.0116273 0.0098479 0.0054091 0.0039236 0.0065692 0.0117235 0.0190579 0.0027983
bp[10] 1.8364588 1.4160375 70810 1.000059 72294 62253 1 0.0053207 -1.2109225 -0.7623808 0.0954488 1.7639634 3.6808375 4.8168022 5.4825704 -0.3584038 1.7639634 4.2744321 0.0185807 0.0115633 0.0075352 0.0056991 0.0105657 0.0169408 0.0273587 0.0041787
bp[8] 1.0829658 0.7700826 55549 1.000055 55771 62853 1 0.0032664 -0.6683257 -0.3913737 0.1181528 1.0690881 2.0722878 2.6346354 2.9516118 -0.1559759 1.0690881 2.3720673 0.0096290 0.0070161 0.0049676 0.0035565 0.0057538 0.0090606 0.0120903 0.0023518
bp[1] -0.5038009 0.8566026 69834 1.000052 70606 66116 1 0.0032412 -2.6475403 -2.2679068 -1.6020696 -0.4812295 0.5641634 1.1117430 1.4219795 -1.9516324 -0.4812295 0.8600996 0.0161158 0.0135247 0.0065357 0.0034433 0.0049128 0.0082105 0.0127338 0.0025912
bp[11] -0.4803541 1.1329087 68533 1.000052 69610 64482 1 0.0043264 -3.3087916 -2.8121146 -1.9318844 -0.4490704 0.9337878 1.6787520 2.0853778 -2.3958794 -0.4490704 1.3262466 0.0174634 0.0149733 0.0083459 0.0044802 0.0071956 0.0096881 0.0178487 0.0036089
bp[22] 1.6767100 0.9289026 60956 1.000048 63729 58882 1 0.0037595 -0.2459579 0.0258624 0.5446929 1.6133656 2.8896076 3.6811541 4.1582541 0.2697442 1.6133656 3.2947503 0.0097227 0.0069500 0.0047321 0.0039789 0.0075126 0.0131919 0.0209844 0.0028828
bp[20] 0.2516845 0.8258300 69082 1.000042 69516 67369 1 0.0031418 -1.7135189 -1.3822578 -0.7957450 0.2527759 1.2991746 1.8762002 2.2079339 -1.1087104 0.2527759 1.6070401 0.0130444 0.0097669 0.0053013 0.0033187 0.0059205 0.0102525 0.0127038 0.0026149
bp[6] -2.5160719 1.2352393 64680 1.000040 68308 59595 1 0.0048559 -5.8580239 -5.2361218 -4.1527289 -2.4031224 -1.0280163 -0.3996788 -0.0804746 -4.7024812 -2.4031224 -0.6830103 0.0233069 0.0174985 0.0094258 0.0053799 0.0064490 0.0082752 0.0104397 0.0037187
bp[15] -2.1629557 1.3011072 68618 1.000040 71058 61314 1 0.0049666 -5.5911018 -4.9751900 -3.8820470 -2.0696193 -0.5768301 0.1138601 0.4918438 -4.4617336 -2.0696193 -0.2048360 0.0268714 0.0175745 0.0110835 0.0055139 0.0063678 0.0102224 0.0118989 0.0038046
bp[18] -0.4157209 0.8552554 70147 1.000037 70918 63734 1 0.0032286 -2.5601584 -2.1731708 -1.5068262 -0.3914754 0.6502427 1.1948892 1.5145900 -1.8606331 -0.3914754 0.9387703 0.0166903 0.0107122 0.0059144 0.0034418 0.0052305 0.0085159 0.0118768 0.0026465
bp[24] 0.0535242 0.8757553 62292 1.000033 62718 64007 1 0.0035085 -1.9514953 -1.6345657 -1.0443626 0.0362416 1.1711558 1.8462487 2.2264183 -1.3635414 0.0362416 1.5118353 0.0123043 0.0090243 0.0059526 0.0039878 0.0063134 0.0104316 0.0169470 0.0028103
bp[14] 0.8371517 0.8520636 65151 1.000024 65852 66382 1 0.0033379 -1.0821988 -0.7750431 -0.2233641 0.8138383 1.9333661 2.5827853 2.9480563 -0.5176359 0.8138383 2.2683222 0.0118233 0.0081046 0.0053730 0.0036978 0.0056672 0.0113982 0.0143183 0.0025429
bp[9] 0.5254456 1.0119958 63071 1.000018 63340 66464 1 0.0040289 -1.8900650 -1.4814139 -0.7632367 0.5312557 1.8032569 2.5122851 2.9020692 -1.1425839 0.5312557 2.1774689 0.0160601 0.0099481 0.0066252 0.0044118 0.0069450 0.0114641 0.0152061 0.0031301
bp[21] 0.5991239 0.7819216 65757 1.000018 66291 67777 1 0.0030476 -1.2017079 -0.9160672 -0.3836045 0.5873325 1.5968681 2.1743505 2.4996688 -0.6646858 0.5873325 1.9023756 0.0093709 0.0087739 0.0050068 0.0032359 0.0058471 0.0088230 0.0121140 0.0023282

\(\phi_{1 \cap 2}\)

\(\alpha_{0}, \alpha_{2}\)

rowname mean sd n_eff Rhat Bulk_ESS Tail_ESS valid se_mean 1% 2.5% 10% 50% 90% 97.5% 99% Q5 Q50 Q95 MCSE_Q1 MCSE_Q2.5 MCSE_Q10 MCSE_Q50 MCSE_Q90 MCSE_Q97.5 MCSE_Q99 MCSE_SD
v[1] -2.725741 0.2406803 10270 1.000598 10293 21057 1 0.0023726 -3.307620 -3.213661 -3.038203 -2.719085 -2.420662 -2.273063 -2.194495 -3.1322 -2.719085 -2.340494 0.0055224 0.0044967 0.0032430 0.0023683 0.0026259 0.0031923 0.0043103 0.0016777
v[2] 2.412404 0.2829256 11810 1.000555 11807 25610 1 0.0026042 1.763262 1.862920 2.051757 2.411075 2.774773 2.972726 3.079254 1.9479 2.411075 2.881321 0.0050346 0.0035228 0.0032298 0.0027134 0.0035238 0.0049149 0.0058329 0.0018415

Submodel 3 - Fecundity

\(\phi_{2 \cap 3}\)

\(\rho\)

rowname mean sd n_eff Rhat Bulk_ESS Tail_ESS valid se_mean 1% 2.5% 10% 50% 90% 97.5% 99% Q5 Q50 Q95 MCSE_Q1 MCSE_Q2.5 MCSE_Q10 MCSE_Q50 MCSE_Q90 MCSE_Q97.5 MCSE_Q99 MCSE_SD
rho 2.312637 0.0909529 9602 1.000547 9694 9244 1 0.0009272 2.107184 2.138144 2.197012 2.310788 2.43065 2.493379 2.532133 2.166746 2.310788 2.463201 0.0034472 0.0024223 0.0016695 0.0008434 0.0018009 0.0027455 0.0045467 0.0006584

Stage 2

PoE

\(\phi_{1 \cap 2}\)

\(\alpha_{0}, \alpha_{2}\)

rowname mean sd n_eff Rhat Bulk_ESS Tail_ESS valid se_mean 1% 2.5% 10% 50% 90% 97.5% 99% Q5 Q50 Q95 MCSE_Q1 MCSE_Q2.5 MCSE_Q10 MCSE_Q50 MCSE_Q90 MCSE_Q97.5 MCSE_Q99 MCSE_SD
v[2] 2.350835 0.2770302 6592 1.000981 6662 6036 1 0.0034068 1.694194 1.803850 1.998920 2.350723 2.701151 2.900099 3.003403 1.891949 2.350723 2.799327 0.0247256 0.0080539 0.0053483 0.0034634 0.0040965 0.0081608 0.0141375 0.0024091
v[1] -2.645742 0.2282998 7227 1.000474 7083 5586 1 0.0026832 -3.206973 -3.115058 -2.947416 -2.637846 -2.357425 -2.220401 -2.148018 -3.037339 -2.637846 -2.285265 0.0112354 0.0055653 0.0041307 0.0026278 0.0036899 0.0055453 0.0113665 0.0018974

\(\phi_{2 \cap 3}\)

\(\rho\)

rowname mean sd n_eff Rhat Bulk_ESS Tail_ESS valid se_mean 1% 2.5% 10% 50% 90% 97.5% 99% Q5 Q50 Q95 MCSE_Q1 MCSE_Q2.5 MCSE_Q10 MCSE_Q50 MCSE_Q90 MCSE_Q97.5 MCSE_Q99 MCSE_SD
V1 2.313578 0.0915351 83292 1.000065 83478 83332 1 0.0003171 2.104902 2.137749 2.19749 2.311566 2.431981 2.495584 2.535545 2.166773 2.311566 2.465292 0.001723 0.0009257 0.0006626 0.0003139 0.000525 0.0009823 0.0017215 0.0002243

\(\psi_{2}\)

rowname mean sd n_eff Rhat Bulk_ESS Tail_ESS valid se_mean 1% 2.5% 10% 50% 90% 97.5% 99% Q5 Q50 Q95 MCSE_Q1 MCSE_Q2.5 MCSE_Q10 MCSE_Q50 MCSE_Q90 MCSE_Q97.5 MCSE_Q99 MCSE_SD
v[6] -0.6862690 0.1519437 3356 1.001784 3433 5883 1 0.0026253 -1.084982 -1.010225 -0.8863896 -0.6751899 -0.49973 -0.4143506 -0.36904 -0.9492081 -0.6751899 -0.4535339 0.00923 0.0064431 0.0038809 0.0025514 0.0027106 0.0028321 0.0033007 0.0018794
NadSurv[4] 5.4508309 1.7705516 16831 1.000509 16916 35665 1 0.0136231 2.000000 2.000000 3.0000000 5.0000000 8.00000 9.0000000 10.00000 3.0000000 5.0000000 8.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0096332
NadSurv[14] 4.6615247 1.6553625 19501 1.000457 19722 44608 1 0.0118111 1.000000 2.000000 3.0000000 5.0000000 7.00000 8.0000000 9.00000 2.0000000 5.0000000 7.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0083518
NadSurv[3] 4.8563762 1.7296525 16615 1.000429 16728 40972 1 0.0133989 1.000000 2.000000 3.0000000 5.0000000 7.00000 8.0000000 9.00000 2.0000000 5.0000000 8.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0094746
Nadimm[18] 3.6809840 1.6649611 25953 1.000427 25686 51819 1 0.0103377 0.000000 1.000000 2.0000000 4.0000000 6.00000 7.0000000 8.00000 1.0000000 4.0000000 7.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0073100
NadSurv[9] 4.1314899 1.5729343 21668 1.000422 21675 41126 1 0.0106908 1.000000 1.000000 2.0000000 4.0000000 6.00000 7.0000000 8.00000 2.0000000 4.0000000 7.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0075596
NadSurv[5] 6.1299732 1.8986578 18143 1.000391 18275 44343 1 0.0140979 2.000000 3.000000 4.0000000 6.0000000 9.00000 10.0000000 11.00000 3.0000000 6.0000000 9.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0099689
NadSurv[13] 4.6098972 1.6268728 19714 1.000378 19797 45754 1 0.0115855 1.000000 2.000000 3.0000000 5.0000000 7.00000 8.0000000 9.00000 2.0000000 5.0000000 7.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0081923
Nadimm[23] 6.9854909 2.2064485 20442 1.000369 20016 33951 1 0.0154385 2.000000 3.000000 4.0000000 7.0000000 10.00000 12.0000000 13.00000 4.0000000 7.0000000 11.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.5000000 0.0109168
Nadimm[13] 5.5518193 1.9976574 22352 1.000367 22248 51226 1 0.0133614 1.000000 2.000000 3.0000000 5.0000000 8.00000 10.0000000 11.00000 2.0000000 5.0000000 9.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0094481
Nadimm[19] 3.2205194 1.5447992 29925 1.000355 29834 49861 1 0.0089275 0.000000 1.000000 1.0000000 3.0000000 5.00000 6.0000000 7.00000 1.0000000 3.0000000 6.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.5000000 0.0000000 0.0063128
NadSurv[6] 6.0853709 1.9210832 17420 1.000354 17493 44450 1 0.0145498 2.000000 3.000000 4.0000000 6.0000000 9.00000 10.0000000 11.00000 3.0000000 6.0000000 9.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0102884
Nadimm[14] 5.3776105 1.9791212 20906 1.000338 20897 51046 1 0.0136903 1.000000 2.000000 3.0000000 5.0000000 8.00000 10.0000000 10.00000 2.0000000 5.0000000 9.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0096806
NadSurv[7] 5.4907995 1.8387224 18956 1.000326 18978 35788 1 0.0133526 2.000000 2.000000 3.0000000 5.0000000 8.00000 9.0000000 10.00000 3.0000000 5.0000000 9.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0094419
NadSurv[8] 4.6568162 1.7023023 20649 1.000320 20646 43061 1 0.0118511 1.000000 2.000000 3.0000000 5.0000000 7.00000 8.0000000 9.00000 2.0000000 5.0000000 8.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0083801
Nadimm[25] 8.9644816 2.6313195 14647 1.000310 14492 31890 1 0.0217464 3.000000 4.000000 6.0000000 9.0000000 12.00000 14.0000000 16.00000 5.0000000 9.0000000 13.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0153773
Nadimm[12] 5.1735920 1.9128637 25200 1.000305 25185 49013 1 0.0120555 1.000000 2.000000 3.0000000 5.0000000 8.00000 9.0000000 10.00000 2.0000000 5.0000000 8.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0085246
Nadimm[11] 4.8188576 1.8597645 24603 1.000299 24668 47314 1 0.0118478 1.000000 2.000000 3.0000000 5.0000000 7.00000 9.0000000 10.00000 2.0000000 5.0000000 8.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0083778
NadSurv[15] 4.5174675 1.6389903 20359 1.000285 20493 45101 1 0.0114645 1.000000 2.000000 2.0000000 4.0000000 7.00000 8.0000000 9.00000 2.0000000 4.0000000 7.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0081067
Nadimm[24] 7.8618431 2.4024294 17992 1.000282 17912 39615 1 0.0178877 3.000000 3.000000 5.0000000 8.0000000 11.00000 13.0000000 14.00000 4.0000000 8.0000000 12.0000000 0.00000 0.5000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0126487
NadSurv[2] 5.2024351 1.8608598 16685 1.000278 16834 39764 1 0.0144102 1.000000 2.000000 3.0000000 5.0000000 8.00000 9.0000000 10.00000 2.0000000 5.0000000 8.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0101898
Nadimm[26] 9.7914479 2.9884284 14502 1.000266 14309 32517 1 0.0247772 4.000000 4.000000 6.0000000 10.0000000 14.00000 16.0000000 17.00000 5.0000000 10.0000000 15.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0175205
Nadimm[5] 7.4730320 2.3407114 17271 1.000251 17181 34559 1 0.0177969 3.000000 3.000000 5.0000000 7.0000000 11.00000 12.0000000 13.00000 4.0000000 7.0000000 11.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.5000000 0.0000000 0.0000000 0.0125845
NadSurv[12] 4.3107155 1.5760094 21816 1.000249 21991 44743 1 0.0106623 1.000000 1.000000 2.0000000 4.0000000 6.00000 8.0000000 8.00000 2.0000000 4.0000000 7.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.5000000 0.0000000 0.0075395
Nadimm[8] 4.9361301 1.9456982 22369 1.000234 22076 43268 1 0.0129732 1.000000 2.000000 3.0000000 5.0000000 7.00000 9.0000000 10.00000 2.0000000 5.0000000 8.0000000 0.00000 0.5000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0091735
Nadimm[9] 4.5422104 1.8319302 23629 1.000233 23522 43326 1 0.0118770 1.000000 1.000000 2.0000000 4.0000000 7.00000 8.0000000 9.00000 2.0000000 4.0000000 8.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0083984
Nadimm[20] 3.5037252 1.5706212 32307 1.000226 32467 59667 1 0.0087339 0.000000 1.000000 2.0000000 3.0000000 6.00000 7.0000000 8.00000 1.0000000 3.0000000 6.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0061759
Nadimm[3] 5.5588696 2.0198787 22002 1.000222 21970 54996 1 0.0135979 1.000000 2.000000 3.0000000 5.0000000 8.00000 10.0000000 11.00000 2.0000000 5.0000000 9.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0096153
NadSurv[24] 6.2931313 1.9161487 16541 1.000218 16507 38271 1 0.0148836 2.000000 3.000000 4.0000000 6.0000000 9.00000 10.0000000 11.00000 3.0000000 6.0000000 9.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0105245
Nadimm[21] 4.5926630 1.7479788 26674 1.000217 26597 49499 1 0.0107010 1.000000 2.000000 2.0000000 4.0000000 7.00000 8.0000000 9.00000 2.0000000 4.0000000 8.0000000 0.00000 0.5000000 0.0000000 0.5000000 0.0000000 0.0000000 0.0000000 0.0075668
Nadimm[7] 6.0377602 2.1474640 19256 1.000215 19266 38424 1 0.0154518 2.000000 2.000000 3.0000000 6.0000000 9.00000 11.0000000 11.00000 3.0000000 6.0000000 10.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.5000000 0.0000000 0.0109262
NadSurv[11] 4.0924463 1.5542426 21446 1.000212 21605 41921 1 0.0106190 1.000000 1.000000 2.0000000 4.0000000 6.00000 7.0000000 8.00000 2.0000000 4.0000000 7.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0075088
Nadimm[15] 5.1316566 1.9449519 22896 1.000211 22758 45295 1 0.0128330 1.000000 2.000000 3.0000000 5.0000000 8.00000 9.0000000 10.00000 2.0000000 5.0000000 8.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0090744
NadSurv[23] 5.4534977 1.7569923 18558 1.000201 18774 39672 1 0.0128813 2.000000 2.000000 3.0000000 5.0000000 8.00000 9.0000000 10.00000 3.0000000 5.0000000 8.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0091591
NadSurv[20] 2.9719986 1.3027720 25112 1.000194 25394 47725 1 0.0082141 0.000000 1.000000 1.0000000 3.0000000 5.00000 6.0000000 6.00000 1.0000000 3.0000000 5.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0058083
Nadimm[2] 5.5000667 2.0648413 22035 1.000191 22113 51874 1 0.0138860 1.000000 2.000000 3.0000000 5.0000000 8.00000 10.0000000 11.00000 2.0000000 5.0000000 9.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0098190
Nadimm[1] 4.6633082 3.1525834 34784 1.000188 36188 62840 1 0.0168993 1.000000 1.000000 1.0000000 4.0000000 9.00000 12.0000000 14.00000 1.0000000 4.0000000 11.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0119497
NadSurv[21] 3.5040252 1.3856827 22466 1.000169 22611 52010 1 0.0092515 1.000000 1.000000 2.0000000 3.0000000 5.00000 6.0000000 7.00000 1.0000000 3.0000000 6.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0065419
NadSurv[19] 2.9996750 1.3419190 23376 1.000167 23519 46175 1 0.0087620 0.000000 1.000000 1.0000000 3.0000000 5.00000 6.0000000 6.00000 1.0000000 3.0000000 5.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0061958
NadSurv[26] 7.9594480 2.2595841 19794 1.000166 19787 47500 1 0.0160462 3.000000 4.000000 5.0000000 8.0000000 11.00000 13.0000000 13.00000 4.0000000 8.0000000 12.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.5000000 0.0113465
NadSurv[16] 4.4061286 1.6045538 21303 1.000166 21480 46086 1 0.0109877 1.000000 1.000000 2.0000000 4.0000000 6.00000 8.0000000 8.00000 2.0000000 4.0000000 7.0000000 0.00000 0.5000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0077696
N1[12] 0.8067570 0.8898625 45978 1.000160 46940 58730 1 0.0041477 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 3.00000 0.0000000 1.0000000 2.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0029329
Nadimm[16] 5.0665283 1.9162455 22569 1.000159 22507 45095 1 0.0127523 1.000000 2.000000 3.0000000 5.0000000 8.00000 9.0000000 10.00000 2.0000000 5.0000000 8.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0090173
N1[11] 0.7447539 0.8544951 44945 1.000159 46607 58301 1 0.0040213 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 3.00000 0.0000000 1.0000000 2.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0028688
Nadimm[17] 4.5196010 1.8215553 22595 1.000154 22346 39371 1 0.0121169 1.000000 1.000000 2.0000000 4.0000000 7.00000 8.0000000 9.00000 2.0000000 4.0000000 8.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0085681
N1[18] 0.5631615 0.7398853 45944 1.000151 46639 53423 1 0.0034509 0.000000 0.000000 0.0000000 0.0000000 2.00000 2.0000000 3.00000 0.0000000 0.0000000 2.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0024401
Nadimm[4] 7.0186176 2.2142808 19248 1.000140 19196 34849 1 0.0159227 2.000000 3.000000 4.0000000 7.0000000 10.00000 12.0000000 13.00000 4.0000000 7.0000000 11.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0112592
NadSurv[18] 3.4831075 1.4523172 23480 1.000134 23680 48595 1 0.0094586 1.000000 1.000000 2.0000000 3.0000000 5.00000 6.0000000 7.00000 1.0000000 3.0000000 6.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0066883
NadSurv[17] 4.0997967 1.5580729 21364 1.000132 21483 42484 1 0.0106618 1.000000 1.000000 2.0000000 4.0000000 6.00000 7.0000000 8.00000 2.0000000 4.0000000 7.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0075392
NadSurv[25] 7.1579829 2.0663293 16739 1.000130 16848 36913 1 0.0159403 3.000000 3.000000 5.0000000 7.0000000 10.00000 11.0000000 12.00000 4.0000000 7.0000000 11.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0112717
Nadimm[10] 4.6617331 1.8415018 25351 1.000128 25410 45143 1 0.0115422 1.000000 1.000000 2.0000000 5.0000000 7.00000 8.0000000 9.00000 2.0000000 5.0000000 8.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.5000000 0.0000000 0.0081617
Nadimm[6] 6.9006200 2.2841271 19225 1.000123 19160 46449 1 0.0164669 2.000000 3.000000 4.0000000 7.0000000 10.00000 12.0000000 13.00000 3.0000000 7.0000000 11.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0116440
NadSurv[10] 4.0286348 1.5295478 23887 1.000120 23879 41149 1 0.0099006 1.000000 1.000000 2.0000000 4.0000000 6.00000 7.0000000 8.00000 2.0000000 4.0000000 7.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0070009
N1[26] 1.5066920 1.2451104 48388 1.000118 49713 68430 1 0.0056569 0.000000 0.000000 0.0000000 1.0000000 3.00000 4.0000000 5.00000 0.0000000 1.0000000 4.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0040001
NadSurv[1] 4.6987266 3.1590419 36483 1.000117 37885 69034 1 0.0165357 1.000000 1.000000 1.0000000 4.0000000 9.00000 12.0000000 14.00000 1.0000000 4.0000000 11.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0116926
N1[23] 1.0755538 1.0285444 44277 1.000117 45446 61798 1 0.0048810 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 4.00000 0.0000000 1.0000000 3.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0034514
N1[25] 1.3867943 1.1833375 42326 1.000110 44142 65414 1 0.0057501 0.000000 0.000000 0.0000000 1.0000000 3.00000 4.0000000 5.00000 0.0000000 1.0000000 4.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0041389
N1[3] 0.8690185 0.9285401 42414 1.000109 43749 57103 1 0.0045031 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 4.00000 0.0000000 1.0000000 3.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0032195
N1[6] 1.0688618 1.0287023 42691 1.000107 44235 58918 1 0.0049736 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 4.00000 0.0000000 1.0000000 3.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0035896
N1[2] 0.8486924 0.9167185 44229 1.000089 45109 57905 1 0.0043576 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 4.00000 0.0000000 1.0000000 3.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0030813
N1[14] 0.8304665 0.9050226 44022 1.000087 45284 59122 1 0.0043106 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 3.00000 0.0000000 1.0000000 3.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.5000000 0.0030509
N1[7] 0.9307465 0.9565341 47056 1.000087 48260 62642 1 0.0044081 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 4.00000 0.0000000 1.0000000 3.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0031170
N1[5] 1.1593996 1.0790903 40776 1.000071 42444 63073 1 0.0053365 0.000000 0.000000 0.0000000 1.0000000 3.00000 4.0000000 4.00000 0.0000000 1.0000000 3.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0037735
Nadimm[22] 5.9618898 1.9911815 27008 1.000067 26868 47699 1 0.0121123 2.000000 2.000000 3.0000000 6.0000000 9.00000 10.0000000 11.00000 3.0000000 6.0000000 9.0000000 0.00000 0.0000000 0.5000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0085648
N1[22] 0.9236545 0.9563472 39615 1.000067 40804 55561 1 0.0048008 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 4.00000 0.0000000 1.0000000 3.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0033947
N1[24] 1.2186109 1.1040302 44237 1.000065 45752 62132 1 0.0052445 0.000000 0.000000 0.0000000 1.0000000 3.00000 4.0000000 4.00000 0.0000000 1.0000000 3.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0037274
NadSurv[22] 4.4507392 1.5627018 20845 1.000065 20893 46495 1 0.0108378 1.000000 2.000000 3.0000000 4.0000000 6.00000 8.0000000 8.00000 2.0000000 4.0000000 7.0000000 0.00000 0.0000000 0.5000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0076636
N1[20] 0.5426105 0.7252949 42570 1.000064 43576 51907 1 0.0035093 0.000000 0.000000 0.0000000 0.0000000 2.00000 2.0000000 3.00000 0.0000000 0.0000000 2.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.5000000 0.0000000 0.0000000 0.0024815
N1[9] 0.7016017 0.8331587 47440 1.000063 48750 57803 1 0.0038259 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 3.00000 0.0000000 1.0000000 2.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0027531
N1[1] 4.6665500 3.1515519 35968 1.000062 37611 64222 1 0.0166137 1.000000 1.000000 1.0000000 4.0000000 9.00000 12.0000000 14.00000 1.0000000 4.0000000 11.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0117478
N1[15] 0.7971982 0.8870331 45341 1.000053 46608 57713 1 0.0041643 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 3.00000 0.0000000 1.0000000 2.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0029466
N1[17] 0.7047436 0.8325624 45662 1.000051 47138 58343 1 0.0038895 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 3.00000 0.0000000 1.0000000 2.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0027623
N1[4] 1.0857710 1.0341532 40187 1.000049 41474 56645 1 0.0051563 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 4.00000 0.0000000 1.0000000 3.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0036778
N1[10] 0.7246112 0.8417330 40869 1.000044 41527 51082 1 0.0041608 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 3.00000 0.0000000 1.0000000 2.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0029422
N1[13] 0.8679851 0.9250754 41967 1.000041 42941 55523 1 0.0045125 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 4.00000 0.0000000 1.0000000 3.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0031909
N1[21] 0.7174942 0.8372835 40717 1.000036 41880 52784 1 0.0041479 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 3.00000 0.0000000 1.0000000 2.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0029330
N1[16] 0.7821891 0.8794729 47440 1.000030 48101 59266 1 0.0040348 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 3.00000 0.0000000 1.0000000 2.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0028531
N1[19] 0.4928830 0.6937206 43028 1.000015 43591 50706 1 0.0033380 0.000000 0.000000 0.0000000 0.0000000 1.00000 2.0000000 3.00000 0.0000000 0.0000000 2.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0023604
N1[8] 0.7521293 0.8611415 45991 1.000012 47072 59563 1 0.0040128 0.000000 0.000000 0.0000000 1.0000000 2.00000 3.0000000 3.00000 0.0000000 1.0000000 2.0000000 0.00000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0028375

Log

\(\phi_{1 \cap 2}\)

\(\alpha_{0}, \alpha_{2}\)

rowname mean sd n_eff Rhat Bulk_ESS Tail_ESS valid se_mean 1% 2.5% 10% 50% 90% 97.5% 99% Q5 Q50 Q95 MCSE_Q1 MCSE_Q2.5 MCSE_Q10 MCSE_Q50 MCSE_Q90 MCSE_Q97.5 MCSE_Q99 MCSE_SD
v[1] -2.711037 0.2369906 57558 1.000070 59143 39544 1 0.0009876 -3.290523 -3.191725 -3.025250 -2.701560 -2.412521 -2.270441 -2.193945 -3.115577 -2.701560 -2.335875 0.0034796 0.0035754 0.0017630 0.0009705 0.0012318 0.0013036 0.0042398 0.0007127
v[2] 2.429981 0.2823230 57432 1.000028 57864 37944 1 0.0011779 1.772455 1.879334 2.072495 2.428945 2.788318 2.995660 3.110664 1.971681 2.428945 2.906384 0.0031161 0.0025336 0.0011746 0.0010960 0.0021679 0.0044464 0.0030344 0.0008579

\(\phi_{2 \cap 3}\)

\(\rho\)

rowname mean sd n_eff Rhat Bulk_ESS Tail_ESS valid se_mean 1% 2.5% 10% 50% 90% 97.5% 99% Q5 Q50 Q95 MCSE_Q1 MCSE_Q2.5 MCSE_Q10 MCSE_Q50 MCSE_Q90 MCSE_Q97.5 MCSE_Q99 MCSE_SD
V1 2.313293 0.0917747 79944 1.000039 79953 77663 1 0.0003245 2.102633 2.13541 2.196671 2.311593 2.431567 2.496874 2.535375 2.165855 2.311593 2.465729 0.0015128 0.0009874 0.0005284 0.0003218 0.0006383 0.0009728 0.0017118 0.0002295

Linear

\(\phi_{1 \cap 2}\)

\(\alpha_{0}, \alpha_{2}\)

rowname mean sd n_eff Rhat Bulk_ESS Tail_ESS valid se_mean 1% 2.5% 10% 50% 90% 97.5% 99% Q5 Q50 Q95 MCSE_Q1 MCSE_Q2.5 MCSE_Q10 MCSE_Q50 MCSE_Q90 MCSE_Q97.5 MCSE_Q99 MCSE_SD
v[2] 2.431417 0.2812618 56392 1.000062 56971 36538 1 0.0011840 1.779163 1.880589 2.074372 2.430782 2.786609 2.990856 3.110918 1.972026 2.430782 2.899752 0.0026286 0.0018991 0.0016091 0.0012908 0.0013210 0.0037523 0.0067270 0.0008648
v[1] -2.711882 0.2361377 57101 1.000035 58735 38589 1 0.0009878 -3.286662 -3.196056 -3.024239 -2.703841 -2.412637 -2.272623 -2.197973 -3.116094 -2.703841 -2.337843 0.0056034 0.0048787 0.0019823 0.0010644 0.0011377 0.0017228 0.0021783 0.0007143

\(\phi_{2 \cap 3}\)

\(\rho\)

rowname mean sd n_eff Rhat Bulk_ESS Tail_ESS valid se_mean 1% 2.5% 10% 50% 90% 97.5% 99% Q5 Q50 Q95 MCSE_Q1 MCSE_Q2.5 MCSE_Q10 MCSE_Q50 MCSE_Q90 MCSE_Q97.5 MCSE_Q99 MCSE_SD
V1 2.313628 0.0913447 80784 1.00007 80875 78634 1 0.0003213 2.106583 2.138034 2.197419 2.311681 2.431457 2.495966 2.535676 2.166966 2.311681 2.465212 0.0012771 0.0008885 0.0007219 0.0003418 0.0006607 0.000957 0.0016921 0.0002273

There are no \(\psi_{2}\) diagnostics for log/linear pooling, as we simply reweight the PoE samples to do log/linear pooling in this example, so the mixing is entirely determined by the mixing of \(\boldsymbol{\phi}\).